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arXiv · 1809.06524

Noncommutative Kn\"{o}rrer periodicity and noncommutative Kleinian singularities

Andrew Conner·Ellen Kirkman·W. Frank Moore·Chelsea Walton
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Abstract

We establish a version of Kn\"{o}rrer's Periodicity Theorem in the context of noncommutative invariant theory. Namely, let $A$ be a left noetherian AS-regular algebra, let $f$ be a normal and regular element of $A$ of positive degree, and take $B=A/(f)$. Then there exists a bijection between the set of isomorphism classes of indecomposable non-free maximal Cohen-Macaulay modules over $B$ and those over (a noncommutative analog of) its second double branched cover $(B^\#)^\#$. Our results use and extend the study of twisted matrix factorizations, which was introduced by the first three authors with Cassidy. These results are applied to the noncommutative Kleinian singularities studied by the second and fourth authors with Chan and Zhang.

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BibTeXRIS

Andrew Conner, Ellen Kirkman, W. Frank Moore, Chelsea Walton. 2018-09-18. Noncommutative Kn\"{o}rrer periodicity and noncommutative Kleinian singularities. https://arxiv.org/abs/1809.06524

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